I need help in Math

Which expressions are equivalent to 2 (three-fourths x + 7) minus 3 (one-half x minus 5)? Check all that apply.

Mariulka [41]

Answer:

$2(\frac{3}{4}x+7)+(-3)(\frac{1}{2}x+(-5))$

$2(\frac{3}{4}x)+2(7)+(-3)(\frac{1}{2}x)+(-3)(-5)$

Step-by-step explanation:

The original expression given in the text is

$2(\frac{3}{4}x+7)-3(\frac{1}{2}x-5)$ (1)

And we want to check to what other expressions is equivalent. First of all, we solve it by writing explicitely each term:

$\frac{3}{2}x+14-\frac{3}{2}x+15$ (2)

Let's verify each of the other expressions separately. For the first one:

$2(\frac{3}{4}x+7)+(-3)(\frac{1}{2}x+(-5))$

We see that this is equivalent to expression (1), since the first half is identical, while in the second one, the combination "+-" can be simply written as "-", so we get

$2(\frac{3}{4}x+7)-3(\frac{1}{2}x-5)$

Which is equivalent to (1).

For the 2nd one:

$2(\frac{3}{4}x)+2(7)+3(\frac{1}{2}x)+3(-5)$

This is not equivalent. In fact, here we have applied the distributive property to each term: however, the 3rd and 4th term are not correct, because the (3) must be negative (-3), as in the original expression.

If we write it explicitely in fact, we get

$\frac{3}{2}x+14+\frac{3}{2}x-15$

Which is different from (2).

For the 3rd one:

$2(\frac{3}{4}x)+2(7)+(-3)(\frac{1}{2}x)+(-3)(-5)$

This one is equivalent. In fact, here we have applied the distributive property correctly. By solvign each term we get:

$\frac{3}{2}x+14-\frac{3}{2}x+15$

8 0

3 years ago

Read 2 more answers

Factorize of 2a³-a²+a-2

IrinaK [193]

<h3>Answer: (a - 1)(2a² + a + 2)</h3>

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Explanation:

Use the rational root theorem to determine this list of possible rational roots: 1, -1, 1/2, -1/2

Plug each possible root one at a time into the original expression given. If the simplified result is 0, then that possible root is an actual root.

If we tried say a = -1, then,

2a³-a²+a-2 = 2(-1)³-(-1)²+(-1)-2 = -6

The result is not zero, so a = -1 is not an actual root.

But if we tried say a = 1, then,

2a³-a²+a-2 = 2(1)³-1²+1-2 = 0

We get 0 so a = 1 is an actual root. I'll let you try the other values, but you should find that a = 1 is the only rational root.

Since a = 1 is a root, this makes (a-1) to be a factor.

From here, use either synthetic or polynomial long division to determine the other factor. Refer to the diagram below for each method.

Regardless of which method you pick, the quotient is 2a² + a + 2 which is the other factor needed. The remainder of 0 tells us we have (a-1) as a factor. For more information, check out the remainder theorem.

5 0

2 years ago

I Hope That This Ain't A Fairytale

inysia [295]

Answer:

what song?

Step-by-step explanation:

is that a song wrely

5 0

3 years ago

How to find average value of a function over a given interval?

Strike441 [17]

f(x)=8x−6f(x)=8x-6 , [0,3][0,3]

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.(−∞,∞)(-∞,∞){x|x∈R}{x|x∈ℝ}f(x)f(x) is continuous on [0,3][0,3].f(x)f(x) is continuousThe average value of function ff over the interval [a,b][a,b] is defined as A(x)=1b−a∫baf(x)dxA(x)=1b-a∫abf(x)dx.A(x)=1b−a∫baf(x)dxA(x)=1b-a∫abf(x)dxSubstitute the actual values into the formula for the average value of a function.A(x)=13−0(∫308x−6dx)A(x)=13-0(∫038x-6dx)Since integration is linear, the integral of 8x−68x-6 with respect to xx is ∫308xdx+∫30−6dx∫038xdx+∫03-6dx.A(x)=13−0(∫308xdx+∫30−6dx)A(x)=13-0(∫038xdx+∫03-6dx)Since 88 is constant with respect to xx, the integral of 8x8x with respect to xx is 8∫30xdx8∫03xdx.A(x)=13−0(8∫30xdx+∫30−6dx)A(x)=13-0(8∫03xdx+∫03-6dx)By the Power Rule, the integral of xx with respect to xx is 12x212x2.A(x)=13−0(8(12x2]30)+∫30−6dx)

3 0

4 years ago

Nik needs to estimate how many books will fit in a bin. Each book is 0.75 feet tall, 0.75 feet wide, and 0.25 feet thick. The bi

cricket20 [7]

Step-by-step explanation:

first you find the volume of a bin.

that is multiplication of 3 dimensions given.

4*4*4=64 cubic feet...

now volume of books..

0.75*0.75.0.25=0.14 cubic feet

now the number of books that will fit the bin=volume of bin/volume of books

64/0.14=455

455 books

7 0

3 years ago

I need help in Math​

I need help in Math